Development of a dual transformation method and its application to electronic and nuclear dynamics in intense laser fields

A dual transformation technique that can deal with awkward Coulomb potentials is developed for electronic wave packet dynamics. The technique consists of the variable transformation of the Hamiltonian and the transformation of the wave function with a normalization constraint. The time evolution is carried out by the alternating-direction implicit method. The operation of the transformed Hamiltonian on the wave function is implemented by using fivepoint finite difference formulas. We apply it to H atom and a realistic 3D model of H+2 . Efficient time evolution schemes are provided by imposing the variable transformations on the following requirements: the transformed wave function is zero and analytic at the nuclei; the equal spacings in the scaled coordinates correspond to grid spacings in the unscaled coordinates that are small near the nuclei (to cope with relatively high momentum components near the nuclei) and are large at larger distances. The validity of the transformations is also enforced by the fact that the missing volume in phase space decreases with decreasing spacings.